Rub the lime juice all over tri tip.
In a small bowl, combine the coffee, brown sugar, dry mustard, black pepper, garlic powder, coriander and Mesquite seasoning. Generously rub the seasoning all over the tri tip. Cover and place in the ice box for at least 12 hours.
Bring the tri tip out of the icebox about 30 minutes before cooking to let it warm close to room temperature.
Heat the grill to approximately 220 to 250 degrees F. I like to use a blend of oak hardwood charcoal and apple wood for flavor. Be sure the grill is cleaned and oiled.
Place the tri tip on the indirect heat side. Close the lid and smoke for approximately 30 to 40 minutes or until the internal temperature reaches about 115 degrees F.
Meanwhile, in a small bowl, combine the special sauce ingredients above. Cover and let place in the icebox until ready to serve.
Remove the tri tip from the grill/smoker and double wrap it in pink butcher paper. Place it back on the indirect side of the heat and cook another 20 minutes or until the internal temperature reaches about 120 degrees. F.
Remove the tri tip from the grill/smoker and let rest about 20 minutes. The internal temperature will climb to about 125 degrees. F. Thinly slice against the grain.
Toast the hamburger buns and place about 4 to 6 ounces of meat on top. Layer with lettuce, purple onion and special sauce. Top with the bun and serve.